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On r*‐sequenceability and symmetric harmoniousness of groups. II
Author(s) -
Wang ChengDe,
Leonard Philip A.
Publication year - 1995
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180030409
Subject(s) - mathematics , prime (order theory) , nilpotent , abelian group , order (exchange) , pure mathematics , product (mathematics) , symmetric group , group (periodic table) , combinatorics , geometry , chemistry , finance , economics , organic chemistry
Abstract In this paper we investigate symmetric harmoniousness of groups and connections of this concept to the R *‐sequenceability of groups. We prove that, under suitable assumptions, the direct product of a symmetric harmonious group with a group that is R *‐sequenceable is R *‐sequenceable; we discuss the symmetric harmoniousness of abelian and of nilpotent groups; we also prove that, for a fixed odd prime p , all but possibly finitely many of the nonabelian groups of order pq ( q prime, q ≡ 1 (mod p )) are symmetric harmonious. © 1995 John Wiley & Sons, Inc.